Skip to main content

Full text of "Analytical Mechanics"

See other formats

(a) POINT OUTSIDE THE SPHERE. In this case R>a.   Therefore the expression for the potential may be put in the form
Therefore outside the shell the potential is the same as if the mass of the shell were concentrated at its center.
(b) POINT WITHIN THE SPHERE. In this case R < a.   Therefore
Therefore within the shell the potential is constant and equals that at the surface.
If H denotes the intensity of the field due to the shell, then
rr        67
=  7 ~  when R >a. = 0   when R < a.
Therefore the shell attracts a particle which is outside with the same force as if all of its mass were concentrated at. its center. On the other hand the shell exerts no force on a particle which is within the shell. The distribution of 7 and H in the field are represented graphically in Fig. 108, where curve (I) represents the potential and (II) the intensity.
2. Find the expressions for the potential and the intensity due to a solid spherical mass.